I dont think thats possible. You can upgrade Hyperion to same OS type as exisiting.
for e.g. If you have Linux, you can upgrade to Linux only.
See this : Upgrading EPM System Products.
I believe both can do better either if its a Linux or Windows but i believe Linux will take care of effective utilisation of memory cache and RAM compared to Windows as there are scenarios that unknown process consuming too much of memory or cpu cycle causing the less availability of resources to the application process (which might be because of Virus,auto upgrades,dependency process etc..) compared to windows 2003 , 2008 gives much of efficiency in using windows env .